Chapter 11, Problem 43SGR

To determine

Find the sum of the series, whose $a_1=8;r=\frac{3}{4}$

Answer to Problem 43SGR

  ${\text{S}}_{\infty }=32$

Explanation of Solution

Given:

Find the sum of the series, whose $a_1=8;r=\frac{3}{4}$

Concept Used:

Find the sum of the series, whose $a_1=8;r=\frac{3}{4}$

Sum of infinite GP series: ${\text{S}}_{\infty }=\frac{a_1}{1-r}$

  $\text{If}0<r<1$ , the sum exists.

Calculation:

  $\begin{array}{l}{a}_1=8;r=\frac{3}{4};\text{find}{\text{S}}_{\infty }\\ {\text{S}}_{\infty }=\frac{a_1}{1-r}=\frac{8}{1-\frac{3}{4}}=\frac{8}{\frac{1}{4}}=8·4=32\end{array}$

Thus, ${\text{S}}_{\infty }=32$